<h2>DESCRIPTION</h2>

<em>i.rectify</em> uses the control points included in the source data 
or identified with the
<a href="wxGUI.gcp.html">Ground Control Points Manager</a>
to calculate a transformation matrix and then converts x,y
cell coordinates to standard map coordinates for each pixel
in the image. The result is a planimetric image with a
transformed coordinate system (i.e., a different coordinate
system than before it was rectified). Supported transformation methods 
are first, second, and third order polynomial and thin plate spline. 
Thin plate spline is recommended for ungeoreferenced satellite imagery 
where ground control points (GCPs) are included. Examples are 
<a href="http://www.gdal.org/frmt_l1b.html">NOAA/AVHRR</a>
and <a href="http://www.gdal.org/frmt_various.html#Envisat">ENVISAT</a> 
imagery which include throusands of GCPs.

<p>
If no ground control points are available, the 
<a href="wxGUI.gcp.html">Ground Control Points Manager</a>
must be run before <em>i.rectify</em>. An image must be
georeferences before it can reside in a standard coordinate
LOCATION, and therefore be analyzed with the other map
layers in the standard coordinate LOCATION. Upon
completion of <em>i.rectify</em>, the rectified image is
deposited in the target standard coordinate LOCATION. This
LOCATION is selected using

<em><a href="i.target.html">i.target</a></em>.

<p>More than one raster map may be rectified at a time. Each cell file
should be given a unique output file name. The rectified image or
rectified raster maps will be located in the target LOCATION when the
program is completed. The original unrectified files are not modified
or removed.

<p>If the <b>-c</b> flag is used, <em>i.rectify</em> will only rectify that
portion of the image or raster map that occurs within the chosen window
region in the target location, and only that portion of the cell
file will be relocated in the target database. It is
important therefore, to check the current mapset window in
the target LOCATION if the <b>-c</b> flag is used.

<p>
If you are rectifying a file with plans to patch it to
another file using the GRASS program <em>r.patch</em>,
choose option number one, the current window in the target
location. This window, however, must be the default window
for the target LOCATION. When a file being rectified is
smaller than the default window in which it is being
rectified, NULLs are added to the rectified file. Patching
files of the same size that contain NULL data,
eliminates the possibility of a no-data line in the patched
result. This is because, when the images are patched, the
NULLs in the image are "covered" with non-NULL pixel
values. When rectifying files that are going to be
patched, rectify all of the files using the same default
window.

<h3>Coordinate transformation</h3>
<p>The desired order of transformation (1, 2, or 3) is selected with the
<b>order</b> option.

The program will calculate the RMSE and check the required number of points.

<h4>Linear affine transformation (1st order transformation)</h4>

<dl>
	<dd> x' = ax + by + c
	<dd> y' = Ax + By + C
</dl>

The a,b,c,A,B,C are determined by least squares regression
based on the control points entered.  This transformation
applies scaling, translation and rotation. It is NOT a
general purpose rubber-sheeting like TPS, nor is it ortho-photo
rectification using a DEM, not second order polynomial,
etc. It can be used if (1) you have geometrically correct
images, and (2) the terrain or camera distortion effect can
be ignored.

<h4>Polynomial Transformation Matrix (2nd, 3d order transformation)</h4>

<em>i.rectify</em> uses a first, second, or third order transformation
matrix to calculate the registration coefficients. The number
of control points required for a selected order of transformation
(represented by n) is

<dl>
<dd>((n + 1) * (n + 2) / 2) 
</dl>

or 3, 6, and 10 respectively. It is strongly recommended
that one or more additional points be identified to allow
for an overly-determined transformation calculation which
will generate the Root Mean Square (RMS) error values for
each included point. The RMS error values for all the
included control points are immediately recalculated when
the user selects a different transformation order from the
menu bar. The polynomial equations are performed using a 
modified Gaussian elimination method.

<h4>Thin plate spline (TPS) transformation</h4>
TPS transformation is selected with the <b>-t</b> flag. This method of
coordinate transformation is recommended for satellite imagery where 
hundreds or thousands of GCPs are included, and for historical printed 
or scanned maps with unknown georeferencing and/or known localized 
distortions. 
<p>
TPS combines a linear affine transformation with individual 
transformation coefficients for each GCP, using the radial basis kernel 
function with the distance <em>dist</em> between any two points:

<dl>
<dd>dist<sup>2</sup> * log(dist)
</dl>

As a consequence, localized distortions can be removed with TPS 
transformation. For example, scan line sensors will have due to the 
changing viewing angle larger distortions towards the end points of the 
scan line than at the center of the scan line. Even higher order 
polynomial transformations are not able to remove these locally 
different distortions, but TPS transformation can. For best results, 
TPS requires an even and, for localized distortions, dense spacing of 
GCPs.

<h3>Resampling method</h3>
<p>The rectified data is resampled with one of seven different methods: 
<em>nearest</em>, <em>bilinear</em>, <em>cubic</em>, <em>lanczos</em>,
<em>bilinear_f</em>, <em>cubic_f</em>, or <em>lanczos_f</em>.
<p>The <em>method=nearest</em> method, which performs a nearest neighbor assignment,
is the fastest of the resampling methods. It is primarily used for
categorical data such as a land use classification, since it will not change
the values of the data cells. The <em>method=bilinear</em> method determines the new
value of the cell based on a weighted distance average of the 4 surrounding
cells in the input map. The <em>method=cubic</em> method determines the new value of
the cell based on a weighted distance average of the 16 surrounding cells in
the input map.  The <em>method=lanczos</em> method determines the new value of
the cell based on a weighted distance average of the 25 surrounding cells in
the input map.
<p>The bilinear, cubic and lanczos interpolation methods are most appropriate for
continuous data and cause some smoothing. These options should not be used
with categorical data, since the cell values will be altered.
<p>In the bilinear, cubic and lanczos methods, if any of the surrounding cells used to
interpolate the new cell value are NULL, the resulting cell will be NULL, even if
the nearest cell is not NULL. This will cause some thinning along NULL borders,
such as the coasts of land areas in a DEM. The bilinear_f, cubic_f and lanczos_f
interpolation methods can be used if thinning along NULL edges is not desired.
These methods "fall back" to simpler interpolation methods along NULL borders.
That is, from lanczos to cubic to bilinear to nearest.
<p>If nearest neighbor assignment is used, the output map has the same raster
format as the input map. If any of the other interpolations is used, the
output map is written as floating point.

<p><!--
Note: In interactive mode it is possible to define a new file name
for the target images. This is (currently) not provided in command line
mode.
-->

<h2>NOTES</h2>

If <em>i.rectify</em> starts normally but after some time the following text is seen:
<br><tt>
ERROR: Error writing segment file
</tt><br>
the user may try the <b>-c</b> flag or the module needs more free space
on the hard drive.


<h2>SEE ALSO</h2>

The GRASS 4 <em>
<a href="https://grass.osgeo.org/gdp/imagery/grass4_image_processing.pdf">Image
Processing manual</a></em>

<p><em>
  <a href="m.transform.html">m.transform</a>,
  <a href="r.proj.html">r.proj</a>,
  <a href="v.proj.html">v.proj</a>,
  <a href="i.group.html">i.group</a>,
  <a href="i.target.html">i.target</a>
  <br>
  <a href="wxGUI.gcp.html">Ground Control Points Manager</a>
</em>


<h2>AUTHORS</h2>

William R. Enslin, 
Michigan State University,
Center for Remote Sensing

<p>Modified for GRASS 5.0 by:<br>
Luca Palmeri (palmeri@ux1.unipd.it)<br>
Bill Hughes<br>
Pierre de Mouveaux (pmx@audiovu.com)
<br>
CMD mode by Bob Covill

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